Russian Federation and China also signed on to the 2015 deal.
European Union diplomatic chief Federica Mogherini said the bloc, as well as Britain, France and Germany, deeply regretted the move by Washington.
The unilateral withdrawal came despite other parties to the agreement - Britain, China, France, Germany, Russia and the European Union - pleading with Trump not to abandon the pact aimed at blocking Iran from acquiring a nuclear weapon.
Trump's withdrawal from a landmark 2015 nuclear agreement in May had already spooked investors and triggered a run on the Iranian rial long before nuclear-related sanctions went back into force.
President TrumpDonald John TrumpLeBron James to produce documentary series "Shut Up and Dribble" for Showtime Rosie O'Donnell leads anti-Trump Broadway sing-along at the White House Study warns of looming potential for runaway global warming MORE in an early morning tweet on Tuesday labeled newly reimposed sanctions on Iran the "most biting ... ever".
Iran is accusing the US of reneging on the nuclear agreement, signed by the Obama administration, and of causing recent Iranian economic unrest.
"In my opinion, there is a good chance of that. We would like to see a change in the regime behavior, and I think the Iranian people are looking for the same thing".
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So-called snapback sanctions, due to come into force early on Tuesday, target Iranian purchases of US dollars, metals trading, coal, industrial software and its auto sector.
Trump's top security adviser on Monday urged Iran to take up an offer of talks with the United States or suffer more pain from economic sanctions, but Iran's president said Washington needed first to prove it can be trusted.
The United States has reimposed economic sanctions on Iran that were originally put in place to pressure the country to limit its nuclear program and later lifted under a 2015 worldwide agreement.
He said Iran's leaders may need to "drink the poison cup" and negotiate with the US.
At the same time, Mr Trump is willing to meet Iranian leaders "at any time" to discuss "a real comprehensive deal that will contain their regional ambitions, will end their malign behaviour, and deny them any path to a nuclear weapon", the officials said. "Negotiations with sanctions doesn´t make sense".
"The world has distanced itself from their hostile policies", Zarif said, adding that they "have become the symbol of mistrust in the world".
Saudi Arabia and Israel, Iran's key regional rivals, are among the only countries to strongly support the reimposition of United States sanctions. "That's the ask", said Pompeo on Sunday ahead of the re-imposition.
US trade with Iran stood at $258 million (Dh948m) in 2016, according to the US Census Bureau, while exports to Iran from the European Union, which will be affected by secondary sanctions, were worth $13 billion a year ago.